113 年 國立臺灣大學會計學系碩士班《成本與管理會計》
第 1 題20 分
Vince Corporation manufactures component No. 86, which is used in the production of smartwatches. Vince is preparing for its 2024 pricing plan. Vince has traditionally used a cost-plus pricing, making a 60% markup on total variable cost to arrive at a reasonable selling price. If Vince continues this pricing policy, it expects sales volume to be 200,000 in 2024. Beginning inventory is the same as ending inventory.
Vince's 2024 cost-plus pricing is based on the following cost behavior assumptions within the company's relevant range. Vince has three cost items: A, which is variable; B, which is fixed; and C, which is semi-variable. The company uses the high-low method and extracted the following cost behavior findings from its accounting records:
- At 180,000 units of activity, Cost A totaled $5,220,000.
- At 140,000 units, the low point during the period, Cost C totaled 3.5 per unit.
- At 160,000 units of activity, the sum of Costs A, B, and C amounted to $8,162,000.
The company, though, has noticed a sizable drop in sales volume during 2023, which it attributes to new entrants in the marketplace. This causes Vince to consider a change in its pricing policy to follow target costing. Vince conducted a market research and found the current prevailing market price to be $66.
Required:
(1) If Vince continues its cost-plus pricing, determine the company's 2024 safety margin in dollars.
(2) If management desires to meet the prevailing market price and maintain the current rate of profit on sales, should the company increase or decrease its total unit costs? By how much?
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一、核心觀念
- 變動費、固定費與半變動費的辨識 – 高低點法求半變動費之固定部與變動部。
- 成本加成定價 – 銷售價格 = 變動成本 + 標準加成(本題 60%)。
- 安全邊際 (Safety Margin) – 實際營收 – 損益兩平營收 (= 總成本)。
- 目標成本 (Target Costing) – 目標價格 = 預期市場價格;
目標利潤率 = 既有成本加成方案之 利潤率,由此求出目標單位成本。
二、解題方法
1. 先算出各成本項目的單位成本
| 成本項目 | 取得資料 | 推導過程 | 單位成本 |
|---|---|---|---|
| A (純變動) | 180,000 單位 → $5,220,000 | 5,220,000 ÷ 180,000 = $29 | $29/單位 |
| C (半變動) | 低點 140,000 單位 → 3.5 | ① 固定總額 = 3.5 × 200,000 = 2,996,000 = 16.4/單位 | 變動部 3.5/單位 |
| B (純固定) | 160,000 單位時,A+B+C 總成本 $8,162,000 | A(160k)=29×160,000=700,000+變動3,324,000 <br> B = 8,162,000‑(4,640,000+3,324,000)= $198,000 | 固定總額 198,000 ÷ 200,000 = $0.99 |
2. 計算總變動成本與總固定成本(以 2024 預估銷售量 200,000 單位為基礎)
- 總變動成本/單位 = A 變動 16.4 = $45.4
- 總固定成本/單位 = C 固定 0.99 = $4.49
單位全成本 = 4.49 = **
第 2 題20 分
The AsiaSteel Corporation is an automotive supplier that uses automatic turning machines to manufacture precision parts from steel bars. AsiaSteel is making two independent decisions: 1. Adoption of JIT inventory system. 2. Outsourcing human recourse (HR).
AsiaSteel's inventory of raw steel averages $400,000. Keith Lin, president of AsiaSteel, and Shaun Wu, AsiaSteel's controller, are concerned about the costs of carrying inventory. The steel supplier is willing to supply steel in smaller lots at no additional charge.
Shaun identifies the following effects of adopting a JIT inventory program to virtually eliminate steel inventory:
- Without scheduling any overtime, lost sales due to stockouts would increase by 25,000 units per year. However, by incurring overtime premiums of $30,000 per year, the increase in lost sales could be reduced to 15,000 units per year. This would be the maximum amount of overtime that would be feasible for AsiaSteel.
- Two warehouses currently used for steel bar storage would no longer be needed. AsiaSteel rents one warehouse from another company under a cancelable leasing arrangement at an annual cost of 3.00 per square foot per year. Insurance and property tax costs totaling $10,000 per year would be eliminated.
AsiaSteel's required rate of return on investment is 15% per year. AsiaSteel's budgeted income statement for the year ending December 31, 2024, (in thousands) is:
Revenues (1,000,000 units)
6,380
2,820
Total costs of goods sold
Gross margin
9,200
2,010
750
Total marketing and distribution costs
2,760
Operating income
$3.040
Required:
(1) Calculate the estimated dollar savings (loss) for the AsiaSteel Corporation that would result in 2024 from the adoption of JIT purchasing.
(2) AsiaSteel is considering whether to outsource its HR activities. Salaried professionals who earn 120,000 would be transferred elsewhere in the organization. Miscellaneous departmental overhead (e.g., supplies, copy charges, overnight delivery) is expected to decrease by 25,000 of corporate overhead, previously allocated to HR, would be picked up by other departments. If AsiaSteel can secure needed HR services locally for $410,000, how much would the company benefit by outsourcing?
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核心觀念
本題為管理會計中極為經典的攸關成本分析(Relevant Cost Analysis)與短期特殊決策題型,主要涵蓋兩大主題:
-
即時生產/採購系統(JIT Purchasing)之成本效益評估:
- 存貨持有成本(Carrying Cost)與資金機會成本:降低存貨所釋放之資金,其機會成本為「平均存貨減少額 必要報酬率」。
- 倉儲成本與機會利益:取消外租倉庫之租金節省、自置倉庫出租之租金收入(機會利益),以及免除之保險費與財產稅。
- 缺貨損失(Stockout Cost)與加班決策最佳化:缺貨損失係以「損失之單位邊際貢獻(Unit Contribution Margin, CM)」衡量。若可透過排定加班降低缺貨量,應比較「排定加班之總成本(加班費 剩餘缺貨損失)」與「不加班之缺貨損失」,選取成本較低之最佳策略。
-
自製或外包決策(Outsourcing / Make-or-Buy Decision):
- 攸關成本(可避免成本, Avoidable Costs):外包後可完全消除之內部成本(如裁撤專業人員之薪資、隨作業減少之部門雜項製造費用)。
- 非攸關成本(不可避免成本, Unavoidable Costs):
- 轉調人員薪資:行政助理轉調至其他部門,公司整體薪資支出並未減少。
- 總公司共同管理費用分攤(Allocated Corporate Overhead):由其他部門承接分攤額,對企業整體現金流出並無影響。
解題方法與詳細推導
第 (1) 小題:採行 JIT 採購制度之估計節省(損失)金額
步驟一:計算產品之單位邊際貢獻(Unit CM)
依據 2024 年預算損益表(銷售量為 1,000,000 單位):
-
單位售價(Unit Selling Price, ):
-
單位變動成本(Unit Variable Cost, ):
- 單位變動製造成本:
- 單位變動行銷與配銷成本:
- 單位變動成本合計:
- 單位變動製造成本:
-
單位邊際貢獻(Unit CM):
步驟二:缺貨因應方案之最佳化評估
採行 JIT 後,評估是否應發生每年 $30,000 之加班津貼:
-
方案 A(不排定加班):
- 缺貨損失量 單位
- 損失邊際貢獻 $$165,250
- 加班成本 $0
- 方案 A 總相關成本 $165,250
-
方案 B(排定加班):
- 缺貨損失量降至 單位
- 損失邊際貢獻 $$99,150
- 加班津貼成本 $30,000
- 方案 B 總相關成本 $$$129,150
決策分析:排定加班(方案 B)可節省淨成本 $$$36,100,故理性管理者在實施 JIT 時必然會選擇排定加班。
步驟三:彙整採行 JIT 制度之攸關效益與攸關成本
- JIT 帶來之相關效益(Annual Benefits / Savings):
- 存貨資金機會成本節省:
- 外租倉庫租金節省(可解約):
- 存貨資金機會成本節省:
第 3 題10 分
Kevin Chen is the management accountant at NTU Bank. He is working with the data science team to use a decision tree for predicting whether a loan will repay or default. Kevin knows that defaulting loans have significantly hurt NTU's profitability.
The team selects a random sample of fourteen loans (eight loans that repaid and six loans that defaulted) from NTU's internal loan database and begins the analysis. The team finds two variables highly related to a default payment: credit score and annual income. The team plots the sample in the below diagram and forms the first node of the decision tree using the first cut: Credit Score=800.
🖼️【此處有附圖,請對照原卷】
(圖表顯示了 14 個點,分為 Repay 和 Default 兩類,橫軸為 Annual Income,縱軸為 Credit Score。其中 Credit Score = 800 是一條水平線,作為決策樹的第一個分割點。)
Required: Calculate the information gain from the first cut.
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核心觀念
本題考查決策樹的資訊增益(Information Gain)。其定義為切割前資料的不純度(Entropy),減去切割後各子集合熵的加權平均:
二分類熵公式為:
其中 代表 Repay, 代表 Default。
解題方法
由圖中 的水平切割線統計:
| 分組 | Repay | Default | 合計 |
|---|---|---|---|
| 6 | 2 | 8 | |
| 2 | 4 | 6 | |
| 合計 | 8 | 6 | 14 |
切割前的熵為:
信用分數高於 的子集合,其熵為:
第 4 題20 分
The Gilbert Company manufactures furniture in two departments: molding and finishing. The company uses the first-in, first-out (FIFO) method of process costing. August data for the finishing department are as follows:
Units of beginning work-in-process inventory 25,000
Percentage completion of beginning work-in-process units 25%
Units started 175,000
Units completed 125,000
Units in ending inventory 50,000
Percentage completion of ending work-in-process units 95%
Spoiled units 25,000
Total costs added during current period:
Direct materials 1,589,000
Manufacturing overhead 207,250
Conversion costs 1,618,750
Conversion costs are added evenly during the process. Direct material costs are added when production is 90% complete. The inspection point is at the 80% stage of production. Normal spoilage is 10% of all good units that pass inspection. Spoiled units are disposed of at zero net disposal value.
Required:
Determine total costs assigned to (1) normal spoilage, (2) abnormal spoilage, (3) units completed and transferred out, and (4) ending work-in process.
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核心觀念
- FIFO 流程成本法:期初在製必須先完成其剩餘工作,期內新增成本只分配給本期完成的等價單位。
- 等價單位 (Equivalent Units):以「材料」與「轉換成本」分別計算,依各階段完成比例折算。
- 正常損耗 (Normal spoilage):視為製造成本的一部份,按正常比例分配。
- 異常損耗 (Abnormal spoilage):以損耗成本列為期間費用,成本仍以已發生的等價單位計算。
- 材料投入時點:生產進度達 90% 時投入;檢驗點在 80%,正常損耗發生於檢驗後,故損耗單位 未取得材料成本。
- 轉換成本於全程均勻加入。
解題步驟
-
確定正常與異常損耗數量
- 合格單位(通過檢驗)=完成並轉出的單位 = 125,000
- 正常損耗 = 10% × 125,000 = 12,500 單位
- 異常損耗 = 總損耗 25,000 – 正常損耗 12,500 = 12,500 單位
-
計算本期等價單位
材料等價單位 轉換等價單位 期初在製 (25,000) 25,000 (需全部材料) 25,000×0.75 = 18,750 本期完成的好單位 (100,000) 100,000 100,000 正常損耗 (12,500) 0 12,500×0.80 = 10,000 異常損耗 (12,500) 0 12,500×0.80 = 10,000 期末在製 (50,000) 50,000 (已超過 90%) 50,000×0.95 = 47,500 合計 175,000 186,250 -
計算本期新增成本
- 材料成本:$1,638,000
- 轉換成本:直接人工 1,540,000 + 轉入成本 $1,618,750 = **
第 5 題15 分
The Hansen Company operates a simple chemical process to convert a single material into three separate items, referred to here as A, B, and C. All three end products are separated simultaneously at a single splitoff point. Products A and B are ready for sale immediately upon splitoff without further processing or any other additional costs. Product C, however, is processed further before being sold because there is no available market price for C at the splitoff point.
During 2020, the selling prices of the items and the total amounts sold were as follows:
A—120 tons sold for 500 per ton
C—475 tons sold for $350 per ton
The total joint manufacturing costs for the year were 100,000 to finish product C. There were no beginning inventories of A, B, or C. At the end of the year, the following ending inventories of completed units were on hand: A, 180 tons; B, 60 tons; C, 25 tons. There was no beginning or ending work in process.
Required:
(1) Allocate the joint costs to Products A, B, and C using the following:
a. Net realizable value (NRV) method
b. Constant gross-margin percentage NRV method
(2) For Product C, compute its gross margin for the year under:
a. NRV method
b. Constant gross-margin percentage NRV method
(3) Assume that the company could produce and sell Product C in the same quantity at the splitoff point without additional costs. Under the sales value at splitoff method, what price should the company set to earn a gross margin percentage of 60 percent for Product C? Show your calculation.
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一、核心觀念
- 共同成本 (Joint Cost):在同一製程的分岔點之前所發生的成本,必須依一定基礎分配給各個最終產品。
- 淨可變現價 (Net Realizable Value, NRV):。
- NRV 配分法:以各產品的 NRV 在全部 NRV 中所佔比例分配共同成本。
- 恆定毛利率 NRV 法:先計算整體的毛利率 ,再使每個產品的毛利率皆等於 ,即
- 銷售價於分岔點法 (Sales‑value‑at‑split‑off):若產品在分岔點即有市場價格,則以該價格乘以產量作為分配基礎。
二、解題步驟與完整計算
1️⃣ 先整理資料
| 產品 | 產量 ( ton ) | 銷售價 / ton | 銷售收入 | 期末庫存 ( ton ) | 期末庫存價值 |
|---|---|---|---|---|---|
| A | 120 (已售) | $750 | 120×750 = $90,000 | 180 | 180×750 = $135,000 |
| B | 340 (已售) | $500 | 340×500 = $170,000 | 60 | 60×500 = $30,000 |
| C | 475 (已售) | $350 | 475×350 = $166,250 | 25 | 25×350 = $8,750 |
- 總產量: ton、 ton、 ton(已售+期末庫存)。
- C 之額外加工成本:$100,000,平均每 ton = 100,000/500 = \200$。
2️⃣ NRV 計算
3️⃣ (1) 共同成本分配
a. NRV 方法
b. 恆定毛利率 NRV 方法
先求整體毛利率
第 6 題15 分
The Finn Company produces cotton/polyester blend T-shirts to supply a custom T-shirt customer. The number of shirts budgeted for the period was 700,000. The company experienced a computer failure and some of the data were lost and could not be recovered. The Finn Company recognize material price variance at the moment of purchase. Data the company were able to recover are shown below:
Direct materials used 800,000 sq. yds.
Direct materials purchased 820,000 sq. yds.
Direct materials price variance 38,400 F
Direct manufacturing labor price variance 2.4 per sq. yd.
Standard quantity of direct materials per T-shirt 1.2 sq. yds.
Standard hour of direct manufacturing labor per T-shirt 0.8 hr
Actual direct manufacturing labor cost 18.06/hr
Required: Calculate the following
(1) Actual price per square yard of direct materials
(2) Actual quantity of shirts produced
(3) Standard direct manufacturing labor rate
(4) Direct manufacturing labor efficiency variance
(5) Sales-volume variance for direct manufacturing labor
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本題主要測試標準成本制度下的各種差異分析,包括材料價格差異、材料效率差異、人工價格差異、人工效率差異及銷售量差異。
核心觀念:
- 標準成本差異 (Variance Analysis): 衡量實際成本與標準成本之間的差異,幫助管理層識別績效和潛在問題。
- 材料價格差異 (Material Price Variance): 實際支付價格與標準價格之間的差異。
- 材料效率差異 (Material Efficiency Variance): 實際使用的材料數量與標準允許使用的材料數量之間的差異。
- 人工價格差異 (Labor Price Variance): 實際支付的人工率與標準人工率之間的差異。
- 人工效率差異 (Labor Efficiency Variance): 實際使用的人工時數與標準允許使用的人工時數之間的差異。
- 銷售量差異 (Sales Volume Variance): 由於實際銷售量與預算銷售量之間的差異,對固定製造費用的影響。
已知資訊:
- 預算產量 (Budgeted Production/Sales) = 700,000 單位 (T-shirts)
- 實際使用材料 (Actual Quantity of Materials Used) = 800,000 sq. yds.
- 實際購買材料 (Actual Quantity of Materials Purchased) = 820,000 sq. yds.
- 材料價格差異 (MPV) = $29,520 F (Favorable)
- 材料效率差異 (MEV) = $38,400 F (Favorable)
- 人工價格差異 (LPV) = $31,800 U (Unfavorable)
- 標準材料價格 (Standard Price of Materials, SPm) = $2.4/sq. yd.
- 標準材料用量 (Standard Quantity of Materials per T-shirt, SQm) = 1.2 sq. yds./T-shirt
- 標準人工工時 (Standard Hours of Labor per T-shirt, SQh) = 0.8 hr/T-shirt
- 實際人工總成本 (Actual Direct Manufacturing Labor Cost) = $9,571,800
- 實際人工率 (Actual Rate of Direct Manufacturing Labor, ARh) = $18.06/hr
問題 (1):實際每平方碼直接材料價格 (Actual Price per Square Yard of Direct Materials, APm)
- 材料價格差異 (MPV) = (APm - SPm) AQm (Actual Quantity Purchased)
- 2.4) \times 820,000$ sq. yds.
- 2.4 \times 820,000$
- 2.436$
答案 (1):$2.436
問題 (2):實際生產的 T-shirt 數量 (Actual Quantity of Shirts Produced)
- 材料效率差異 (MEV) = (SQm Actual Production Quantity - AQm Used) SPm
- 2.4/sq. yd.$
- Actual Production = T-shirts
答案 (2):680,000
問題 (3):標準直接人工率 (Standard Direct Manufacturing Labor Rate, SPh)
-
人工價格差異 (LPV) = (ARh - SPh) AH (Actual Hours)
-
18.06/hr - SPh) \times AH$
-
我們需要先計算實際工時 (AH)。
-
實際人工總成本 = 實際人工率 實際工時
-
18.06/hr \times AH$
-
hours.
-
現在代入 LPV 公式:
-
18.06 - SPh) \times 530,000$
-
-